10,195 research outputs found
Large Zero Autocorrelation Zone of Golay Sequences and -QAM Golay Complementary Sequences
Sequences with good correlation properties have been widely adopted in modern
communications, radar and sonar applications. In this paper, we present our new
findings on some constructions of single -ary Golay sequence and -QAM
Golay complementary sequence with a large zero autocorrelation zone, where
is an arbitrary even integer and is an arbitrary integer.
Those new results on Golay sequences and QAM Golay complementary sequences can
be explored during synchronization and detection at the receiver end and thus
improve the performance of the communication system
Exact solutions for KPZ-type growth processes, random matrices, and equilibrium shapes of crystals
Three models from statistical physics can be analyzed by employing space-time
determinantal processes: (1) crystal facets, in particular the statistical
properties of the facet edge, and equivalently tilings of the plane, (2)
one-dimensional growth processes in the Kardar-Parisi-Zhang universality class
and directed last passage percolation, (3) random matrices, multi-matrix
models, and Dyson's Brownian motion. We explain the method and survey results
of physical interest.Comment: Lecture Notes: Fundamental Problems in Statistical Mechanics XI,
Leuven, September 4 - 16, 200
Local limit theorems and mod-phi convergence
We prove local limit theorems for mod-{\phi} convergent sequences of random
variables, {\phi} being a stable distribution. In particular, we give two new
proofs of a local limit theorem in the framework of mod-phi convergence: one
proof based on the notion of zone of control, and one proof based on the notion
of mod-{\phi} convergence in L1(iR). These new approaches allow us to identify
the infinitesimal scales at which the stable approximation is valid. We
complete our analysis with a large variety of examples to which our results
apply, and which stem from random matrix theory, number theory, combinatorics
or statistical mechanics.Comment: 35 pages. Version 2: improved presentation, in particular for the
examples in Section
Segmentation of Fault Networks Determined from Spatial Clustering of Earthquakes
We present a new method of data clustering applied to earthquake catalogs,
with the goal of reconstructing the seismically active part of fault networks.
We first use an original method to separate clustered events from uncorrelated
seismicity using the distribution of volumes of tetrahedra defined by closest
neighbor events in the original and randomized seismic catalogs. The spatial
disorder of the complex geometry of fault networks is then taken into account
by defining faults as probabilistic anisotropic kernels, whose structures are
motivated by properties of discontinuous tectonic deformation and previous
empirical observations of the geometry of faults and of earthquake clusters at
many spatial and temporal scales. Combining this a priori knowledge with
information theoretical arguments, we propose the Gaussian mixture approach
implemented in an Expectation-Maximization (EM) procedure. A cross-validation
scheme is then used and allows the determination of the number of kernels that
should be used to provide an optimal data clustering of the catalog. This
three-steps approach is applied to a high quality relocated catalog of the
seismicity following the 1986 Mount Lewis () event in California and
reveals that events cluster along planar patches of about 2 km, i.e.
comparable to the size of the main event. The finite thickness of those
clusters (about 290 m) suggests that events do not occur on well-defined
euclidean fault core surfaces, but rather that the damage zone surrounding
faults may be seismically active at depth. Finally, we propose a connection
between our methodology and multi-scale spatial analysis, based on the
derivation of spatial fractal dimension of about 1.8 for the set of hypocenters
in the Mnt Lewis area, consistent with recent observations on relocated
catalogs
Theory of optimal orthonormal subband coders
The theory of the orthogonal transform coder and methods for its optimal design have been known for a long time. We derive a set of necessary and sufficient conditions for the coding-gain optimality of an orthonormal subband coder for given input statistics. We also show how these conditions can be satisfied by the construction of a sequence of optimal compaction filters one at a time. Several theoretical properties of optimal compaction filters and optimal subband coders are then derived, especially pertaining to behavior as the number of subbands increases. Significant theoretical differences between optimum subband coders, transform coders, and predictive coders are summarized. Finally, conditions are presented under which optimal orthonormal subband coders yield as much coding gain as biorthogonal ones for a fixed number of subbands
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